Robust spin squeezing from the tower of states of $U(1)$-symmetric spin
Hamiltonians
- URL: http://arxiv.org/abs/2103.07354v2
- Date: Fri, 25 Feb 2022 21:04:04 GMT
- Title: Robust spin squeezing from the tower of states of $U(1)$-symmetric spin
Hamiltonians
- Authors: Tommaso Comparin, Fabio Mezzacapo, Tommaso Roscilde
- Abstract summary: We show that Spin squeezing can be generated via the non-linear, entangling evolution of an initially factorized spin state.
Our results connect quantum simulation with quantum metrology by unveiling the squeezing power of a large variety of Hamiltonian dynamics.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Spin squeezing - a central resource for quantum metrology - can be generated
via the non-linear, entangling evolution of an initially factorized spin state.
Here we show that robust (i.e. persistent) squeezing dynamics is generated by a
very large class of $S=1/2$ spin Hamiltonians with axial symmetry, in
relationship with the existence of a peculiar structure of the low-lying
Hamiltonian eigenstates - the so-called Anderson's tower of states. Such states
are fundamentally related to the appearance of spontaneous symmetry breaking in
quantum systems; and, for models with sufficiently high connectivity, they are
parametrically close to the eigenstates of a planar rotor (Dicke states), in
that they feature an anomalously large value of the total angular momentum. Our
central insight is that, starting from a coherent spin state, a generic
$U(1)$-symmetric Hamiltonian featuring the Anderson's tower of states generates
the same squeezing evolution at short times as the one governed by the
paradigmatic one-axis-twisting (or planar-rotor) model of squeezing dynamics.
The full squeezing evolution of the planar-rotor model is seemingly reproduced
for interactions decaying with distance $r$ as $r^{-\alpha}$ when $\alpha <
5d/3$ in $d$ dimensions. Our results connect quantum simulation with quantum
metrology by unveiling the squeezing power of a large variety of Hamiltonian
dynamics that are currently implemented by different quantum simulation
platforms.
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